Well, Geddy went from a Ric to a Jazz, and he still sounds like.....Geddy. Still, I'm not so sure that just anyone can get similar tones out of the two.
Geddy's jazz has a short in the bridge pickup, which produces similar effects to the caps on the bridge pickup in 70's 4001's. So yes, his basses sound extremely similar.
Still, yes, the most similar bass I've ever played in terms of sound to a Rickenbacker was a Fender Jazz. Wasn't exactly the same, but the same kind of sound.